POSSIBLE TEST QUESTIONS

Many test questions will be selected from the following list. The key to doing well in the class is to do as many of these exercises as possible. (The list will be updated as we go along.) Once you have done all these problems, then you should work other exercises for additional practice.

 Chapter 3, Groups: 6, 12, 14, 17, 24, 25, 26, 27, 28, 29, 30, 31, 32, 35, 36, 37, 38, 39, 40, 43, 44, 45, 46, 47, 48, 50, 51, 52, 53 Chapter 4, Cyclic Groups: 2, 5, 8, 10, 11, 12, 23, 24, 25, 26, 27, 28, 31, 33, 37, 38 Chapter 5, Permutation Groups: 7, 17, 18, 22, 27 Chapter 6, Cosets and Lagrange's Theorem: 3, 4, 9, 12, 14, 16, 17, 18, 21 Chapter 9, Isomorphisms: 2, 7, 8, 9, 16, 18, 22, 26, 27, 48, 50, 52 Chapter 10, Homomorphisms: 5, 6, 8, 10, 12, 14, 15, 16, 18, 23, 24, 27, 32 Chapter 12, Structure of Groups: 1, 2, 3, 5, 6, 8 Chapter 15, Rings: 2, 3, 7, 8, 11, 16, 17, 18, 19bc, 20, 25, 27, 28, 29, 36, 39 Chapter 16, Polynomials: 1, 2, 3, 6, 7, 9, 10, 12, 13, 15, 17, 23, 27

You should also know and internalize (not memorize) the following results. Although it is a good idea to have a rudimentary idea of how the proofs work, the main thing is that you be able to apply these results when necessary to solve other problems. You should also know the definitions of all the terms which appear in these results.

 Proposition 3.1 Proposition 3.2 Proposition 3.3 Proposition 3.4 Proposition 3.5 Proposition 3.6 Proposition 3.7 Theorem 3.8 Proposition 3.9 Proposition 3.10 Theorem 4.1 Theorem 4.2 Theorem 4.3 Corollary 4.4 Theorem 4.6 Corollary 4.7 Proposition 4.10 Theorem 5.1 Theorem 5.3 Theorem 5.4 Theorem 5.6 Theorem 5.7 Proposition 5.8 Lemma 6.1 Theorem 6.3 Theorem 6.5 Corollary 6.6 Corollary 6.7 Corollary 6.8 Theorem 9.1 Theorem 9.2 Theorem 9.3 Theorem 9.4 Theorem 9.5 Theorem 9.6 Theorem 10.1 Theorem 10.2 Proposition 10.3 Theorem 10.4 Theorem 10.9 Theorem 12.3 Theorem 12.5 Proposition 15.1 Proposition 15.2 Proposition 15.3 Theorem 15.4 Proposition 15.6 Proposition 15.7 Proposition 15.8 Theorem 15.9 Theorem 15.10 Theorem 15.11 Theorem 15.15 Theorem 15.16 Theorem 16.1 Proposition 16.2 Theorem 16.4 Corollary 16.5 Corollary 16.6 Theorem 16.12 Theorem 16.13